Inspired by the rich physics of twisted 2D bilayer moire systems, we study Coulomb interacting systems subjected to two overlapping finite ID lattice potentials of unequal periods through exact numerical diagonalization. Unmatching underlying lattice periods lead to a 1D bichromatic {\textquotedblleft}moire{\textquotedblright} superlattice with a large unit cell and consequently a strongly flattened band, exponentially enhancing the effective dimensionless electron-electron interaction strength and manifesting clear signatures of enhanced Mott gaps at discrete fillings. An important nonperturbative finding is a remarkable fine-tuning effect of the precise lattice commensuration, where slight variations in the relative lattice periods may lead to a suppression of the correlated insulating phase, in qualitative agreement with the observed fragility of the correlated insulating phase in twisted bilayer graphene. Our predictions, which should be directly verifiable in bichromatic optical lattices, establish that the competition between interaction and incommensuration is a key element of the physics of moire superlattices.

}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.126.036803}, author = {Vu, DinhDuy and Sankar Das Sarma} } @article { WOS:000707469900008, title = {Superconductors with anomalous Floquet higher-order topology}, journal = {Phys. Rev. B}, volume = {104}, number = {14}, year = {2021}, month = {OCT 11}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We develop a general theory for two-dimensional (2D) anomalous Floquet higher-order topological superconductors (AFHOTSCs), which are dynamical Majorana-carrying phases of matter with no static counterpart. Despite the triviality of its bulk Floquet bands, an AFHOTSC generically features the simultaneous presence of corner-localized Majorana modes at both zero and pi/T quasienergies, a phenomenon beyond the scope of any static topological band theory. We show that the key to AFHOTSCs is their unavoidable singular behavior in the phase spectrum of the bulk time-evolution operator. By mapping such evolution-phase singularities to the stroboscopic boundary signatures, we classify 2D AFHOTSCs that are protected by a rotation group symmetry in symmetry class D. We further extract a higher-order topological index for unambiguously predicting the presence of Floquet corner Majorana modes, which we confirm numerically. Our theory serves as a milestone towards a dynamical topological theory for Floquet superconducting systems.}, issn = {2469-9950}, doi = {10.1103/PhysRevB.104.L140502}, author = {Vu, DinhDuy and Zhang, Rui-Xing and Yang, Zhi-Cheng and Das Sarma, S.} } @article {vu_collective_2020, title = {Collective ground states in small lattices of coupled quantum dots}, journal = {Phys. Rev. Res.}, volume = {2}, number = {2}, year = {2020}, note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article}, month = {apr}, abstract = {Motivated by recent developments on the fabrication and control of semiconductor-based quantum dots, we theoretically study a finite system of tunnel-coupled quantum dots with the electrons interacting through the long-range Coulomb interaction. When the interelectron separation is large and the quantum dot confinement potential is weak, the system behaves as an effective Wigner crystal with a period determined by the electron average density with considerable electron hopping throughout the system. For stronger periodic confinement potentials, however, the system makes a crossover to a Mott-type ground state where the electrons are completely localized at the individual dots with little interdot tunneling. In between these two phases, the system is essentially a strongly correlated electron liquid with intersite electron hopping constrained by strong Coulomb interaction. We characterize this Wigner-Mott-liquid quantum crossover with detailed numerical finite-size diagonalization calculations of the coupled interacting quantum dot system, showing that these phases can be smoothly connected by tuning the system parameters. Experimental feasibility of observing such a hopping-tuned Wigner-Mott-liquid crossover in currently available semiconductor quantum dots is discussed. In particular, we connect our theoretical results to recent quantum-dot-based quantum emulation experiments where a collective Coulomb blockade was demonstrated. We discuss realistic disorder effects on our theoretical findings. One conclusion of our work is that experiments must explore lower density quantum dot arrays in order to clearly observe the Wigner phase although the Mott-liquid crossover phenomenon should already manifest itself in the currently available quantum dot arrays. We also suggest a direct experimental electron density probe, such as atomic force microscopy or scanning tunneling microscopy, for a clear observation of the effective Wigner crystal phase.

}, doi = {10.1103/PhysRevResearch.2.023060}, author = {Vu, DinhDuy and Das Sarma, Sankar} } @article {vu_time-reversal-invariant_2020, title = {Time-reversal-invariant {C}-2-symmetric higher-order topological superconductors}, journal = {Phys. Rev. Res.}, volume = {2}, number = {4}, year = {2020}, note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article}, month = {nov}, abstract = {We propose a minimal lattice model for two-dimensional class DIII superconductors with C-2-protected higher-order topology. Although this class of superconductors cannot be topologically characterized by symmetry eigenvalues at high-symmetry momenta, we propose a simple Wannier-orbital-based real-space diagnosis to unambiguously capture the corresponding higher-order topology. We further identify and characterize a variety of conventional topological phases in our minimal model, including a weak topological superconductor and a nodal topological superconductor with chiral-symmetry protection. The disorder effect is also systematically studied to demonstrate the robustness of higher-order bulk-boundary correspondence. Our theory lays the groundwork for predicting and diagnosing C-2-protected higher-order topology in class DIII superconductors.}, doi = {10.1103/PhysRevResearch.2.043223}, author = {Vu, DinhDuy and Zhang, Rui-Xing and Das Sarma, S.} } @article {vu_tunneling_2020, title = {Tunneling conductance of long-range {Coulomb} interacting {Luttinger} liquid}, journal = {Phys. Rev. Res.}, volume = {2}, number = {2}, year = {2020}, note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article}, month = {may}, abstract = {The theoretical model of the short-range interacting Luttinger liquid predicts a power-law scaling of the density of states and the momentum distribution function around the Fermi surface, which can be readily tested through tunneling experiments. However, some physical systems have long-range interaction, most notably the Coulomb interaction, leading to significantly different behaviors from the short-range interacting system. In this paper, we revisit the tunneling theory for the one-dimensional electrons interacting via the long-range Coulomb force. We show that, even though in a small dynamic range of temperature and bias voltage the tunneling conductance may appear to have a power-law decay similar to short-range interacting systems, the effective exponent is scale dependent and slowly increases with decreasing energy. This factor may lead to the sample-to-sample variation in the measured tunneling exponents. We also discuss the crossover to a free Fermi gas at high energy and the effect of the finite size. Our work demonstrates that experimental tunneling measurements in one-dimensional electron systems should be interpreted with great caution when the system is a Coulomb Luttinger liquid.}, doi = {10.1103/PhysRevResearch.2.023246}, author = {Vu, DinhDuy and Iucci, Anibal and Das Sarma, S.} }